Shape-morphing finds widespread utility, from the deployment of small stents and large solar sails to actuation and propulsion in soft robotics. Origami structures provide a template for shape-morphing, but rules for designing and folding the structures are challenging to integrate into broad and versatile design tools. Here, we develop a sequential two-stage optimization framework to approximate a general surface by a deployable origami structure. The optimization is performed over the space of all possible rigidly and flat-foldable quadrilateral mesh origami. So, the origami structures produced by our framework come with desirable engineering properties: they can be easily manufactured on a flat reference sheet, deployed to their target state by a controlled folding motion, then to a compact folded state in applications involving storage and portability. The attainable surfaces demonstrated include those with modest but diverse curvatures and unprecedented ones with sharp ridges. The framework provides not only a tool to design various deployable and retractable surfaces in engineering and architecture, but also a route to optimizing other properties and functionality.
Reprogrammable origami through bistable buckled hinges
J.A.Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学生物工程与应用科学学院）；PSL University（巴黎文理研究大学）；Department of Precision and Microsystems Engineering, Delft University of Technology（代尔夫特理工大学精密与微系统工程系）
An exact dimension-reduced dynamic theory for developable surfaces and curve-fold origami
State Key Laboratory for Turbulence and Complex Systems, School of Mechanics and Engineering Science, Peking University（湍流与复杂系统国家重点实验室，力学与工程科学学院，北京大学）；School of Mechanics and Engineering Science, Peking University（力学与工程科学学院，北京大学）；HEDPS, CAPT and IFSA, Collaborative Innovation Center of MoE, Peking University（高能密度物理研究所，中心，前沿科学研究中心，教育部协同创新中心，北京大学）
